venomx8e0b

2023-03-13

Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III

neizhojen50q

(C) Explanation: Noting that a function is differentiable at a point if

the given information effectively is that is differentiable at and that .Now, looking at the statements:
I: True
A function's differentiability at a point implies its continuity at that point.
II: True
The given information matches the definition of differentiability at .
III: False
The derivative of a function is not necessarily continuous, a classic example being , which is differentiable at , but whose derivative has a discontinuity at .

Do you have a similar question?